Range of vision on a clear day depends on the topology of the world you are in, and how high you are.
If the world is flat, it would probably be possible to see all the way till the next mountain blocked you, meaning if you were on the highest mountain, you'd see the entire world.
If the world is a globe you can calculate the distance by using trigonometri. The direct distance you could see (which is very close to the distance running along the surface of the globe if the object isn't highly elevated) can be calculated by the following equation:
D=sqrt(r+h)²-r²) so, D=sqrt(2hr+h²)
Where D is the distance you can see, r is the radius of the globe, and h is your height above sea level.
This assumes either you or your target is at sea level, or close enough to sea level that it doesn't matter.
If both of them aren't you can get the farthest distance you can see a taller object, simply by adding the distance you would be able to see the sea level from object A to the the distance you could see sea level from Object B.
OR
D=D1+D2=sqrt(2h*r1+h²)+sqrt(2h*r2+h²)
That probably wasn't what you were asking, but apart from that I really can't tell you how far you can see in a fog. Some light fogs you can see as far as 200 meters in, others you can't see more than 50 meters. Light sources can be seen further off (very far during the night), and small objects are harder to spot. In most cases I would make it as problems to the perception tests rather than just tell people that they "can't see"